What is the term for giving an action or phenomenon somebody's name, e.g. "Doing a Lord Lucan"?
Solution 1:
The term for this concept is eponym. From TheFreeDictionary:
ep·o·nym (p-nm) n.
1. A word or name derived from the name of a person. The words atlas, bowdlerize, and Turing machine are eponyms.
2. A person whose name is or is thought to be the source of the name of something.
I don't know if there's a verb that describes this process. Probably "making an eponym" would be the closest.
Edit: @JSBangs deftly suggests eponymize in the comments below, and that sounds good to me.